When an experiment is conducted for purposes which include fitting a particular model to the data, then the ‘optimal’ experimental design is highly dependent upon the model assumptions – linearity of the response function, independence and homoscedasticity of the errors, etc. When these assumptions are violated the design can be far from optimal, and so a more robust approach is called for. We should seek a design which behaves reasonably well over a large class of plausible models.

I will review the progress which has been made on such problems, in a variety of experimental and modelling scenarios – prediction, extrapolation, discrimination, survey sampling, dose-response, machine learning, etc.

In Optimal Experimental Design, we usually assume the normal distribution for the responses, hence the errors have a normal distribution.

The Central Limit Theorem ensure us that, if the ­sample size is big enough, this assumption is not a problem, but are not always able to do so. Therefore, the behaviour of the optimal experimental design is approached for others common probabiity distributions commonly used in various areas of knowledge. We compute and compare D-optimal designs for different linear and non-linear models assuming different probability distributions.

Mixture experiments analyse systems defined over a simplex-shaped experimental region. Mixture design background has mainly been based on a classical design approach. There is not much literature for mixtures in the context of optimal experimental design, specifically for non-linear models. Analytical solutions can only be found on examples where strict assumptions have to be included. They are far from realistic scenarios. In spite of this simplification, numerical methods are needed to construct optimal designs. Under this framework, it is necessary to develop general optimization techniques in order to find optimal solutions for these problems. Two efficient algorithms are proposed in this paper for computing exact D-optimal designs in order to deal with the special nature of mixture experiments. They are based on a multiplicative algorithm and a genetic algorithm. Several examples illustrate the enhanced results achieved by these new methods.